Rectangular Prism Volume Calculator

Rectangular prism volume calculator computes V = length x width x height (L x W x H). A box measuring 4 x 3 x 2 has volume 24 cubic units. Also calculates surface area SA = 2(lw + lh + wh) and space diagonal = sqrt(l^2 + w^2 + h^2). Works for boxes, rooms, aquarium tanks, and shipping containers.

Enter Values

Result

Enter values above and click Calculate to see your result.

AI Assistant

Ask about this calculator

I can help you understand the rectangular prism volume calculator formula, interpret your results, and answer follow-up questions.

Try asking

Formula

#
Core Formula
V=L×W×HV = L \times W \times H

How it works: Multiply the three perpendicular dimensions (length, width, height) to get volume in cubic units.

Worked Example

Find the volume of a box measuring 4 x 3 x 2.
1Step 1: V = L x W x H = 4 x 3 x 2 = 24 cubic units.
2Step 2: Surface area = 2(LW + LH + WH) = 2(12 + 8 + 6) = 2 x 26 = 52 square units.
3Step 3: Space diagonal = sqrt(L^2 + W^2 + H^2) = sqrt(16 + 9 + 4) = sqrt(29) = 5.39 units. Practical example: a room 12 ft x 10 ft x 8 ft = 960 cubic feet. To convert to gallons: 960 x 7.48 = 7,181 gallons.

Rectangular Prism Volume and Surface Area

A rectangular prism (also called a cuboid or box) has six rectangular faces. Its volume is the product of its three dimensions.

  • Volume = Length x Width x Height. A 4 x 3 x 2 box has volume 24 cubic units
  • Surface area = 2(LW + LH + WH). Same box: 2(12 + 8 + 6) = 52 square units
  • Space diagonal (corner to opposite corner) = sqrt(L^2 + W^2 + H^2)
  • Units must be consistent: all in cm gives cm^3, all in feet gives cubic feet. 1 cubic foot = 7.48 gallons

This is the most common volume formula in everyday use: room sizing for HVAC, concrete estimation, shipping calculations, and aquarium capacity all use L x W x H.

You can also calculate changes using our Rectangle Volume Calculator, LxWxH Calculator, Shipping Box Volume Calculator or Cube Volume Calculator.

Frequently Asked Questions

How do I calculate the volume of a room?

Measure length, width, and height in the same unit (feet or meters), then multiply: V = L x W x H. A room 12 ft x 10 ft x 8 ft = 960 cubic feet. This is useful for HVAC sizing, where you need about 1 ton of AC per 400-600 sq ft depending on climate.

Is rectangular prism volume the same as L x W x H?

Yes, exactly. A rectangular prism, cuboid, and box all use the same formula: Volume = Length x Width x Height. The order of multiplication does not matter (4 x 3 x 2 = 2 x 3 x 4 = 24).

How do I convert cubic feet to gallons?

Multiply cubic feet by 7.481 to get US gallons. A rectangular tank 3 ft x 2 ft x 1.5 ft = 9 cubic feet = 67.3 gallons. For liters: multiply cubic feet by 28.317. For cubic meters to liters: multiply by 1,000.

What is the surface area of a rectangular prism?

Surface area = 2(LW + LH + WH). A box measuring 4 x 3 x 2 has SA = 2(12 + 8 + 6) = 52 square units. Surface area tells you how much material you need to wrap, paint, or cover the box.

What units should I use?

Use consistent units for all three dimensions. If you enter centimeters, the volume is in cubic centimeters (cm^3). If you enter feet, the volume is in cubic feet. Never mix units (e.g., length in meters and width in feet) without converting first.

What is the difference between a rectangular prism and a cuboid?

They are the same shape. A rectangular prism, cuboid, and box all refer to a three-dimensional solid with six rectangular faces and right angles at every corner. A cube is a special case where all three dimensions (length, width, height) are equal. The volume formula V = L x W x H applies to all of these.

Is it possible to embed the Rectangular Prism Volume Calculator on another website?

Yes, embedding the Rectangular Prism Volume Calculator is free. Hit the "Embed" button on this page, adjust the width, height, and theme, then grab the iframe code. It works on WordPress, Wix, Squarespace, Shopify, and plain HTML pages. No registration needed. Full instructions at calculory.com/services/embed-calculators.

Accurate and Reliable

All calculations run locally. Precise geometric calculations with visual explanations.

Verified Precision

Precise Geometry Calculations Powered by Calculory AI